Partial Group (co)actions of Hopf Group Coalgebras

Abstract

We will develop partial group (co)actions of a Hopf group coalgebra on a family of algebras by introducing partial group entwining structure.   Then  we give necessary and sufficient conditions for a family of  functors from  the category of partial group entwining modules to the category of modules  over a suitable algebra to be separable. Also, the applications of our results are considered.